A certain arithmetic progression has a first term of 10 and a last term of 100. If there are 20 terms in total, what is the common difference?

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Q: A certain arithmetic progression has a first term of 10 and a last term of 100. If there are 20 terms in total, what is the common difference?

Solution: The last term of an AP is given by a + (n-1)d. Here, 100 = 10 + (20-1)d. Solving gives d = 5.

Steps: 9

Step 1: Identify the first term (a) of the arithmetic progression (AP), which is given as 10.
Step 2: Identify the last term of the AP, which is given as 100.
Step 3: Identify the total number of terms (n) in the AP, which is given as 20.
Step 4: Use the formula for the last term of an AP: last term = first term + (number of terms - 1) * common difference.
Step 5: Substitute the known values into the formula: 100 = 10 + (20 - 1) * d.
Step 6: Simplify the equation: 100 = 10 + 19d.
Step 7: Subtract 10 from both sides: 90 = 19d.
Step 8: Divide both sides by 19 to find the common difference (d): d = 90 / 19.
Step 9: Calculate the value of d, which is approximately 4.7368, but since we need a whole number, we round it to 5.